Installation:
Put textures.ini and the folders in PPSSPP\MemStick\PSP\TEXTURES\*GAME_ID* - with GAME_ID being the game's ID displayed in PPSSPP's titlebar when you run the game (example: ULUS10160).
In PPSSPP, turn on the Replace Textures option in Settings > Tools > Developer Tools

Screenshots: (click on them to see high resolution comparisons with the original)
Liberty City Stories:
Vice City Stories:

No, I tried some of the GTA III Xbox grass/road textures, but they clash badly with the other low res textures and low poly models IMO. Perhaps it'd look good if someone did a complete overhaul, but I'm not going to (I don't think I'll be updating this anymore).
Though if someone else would like to do that, they're free to use any or all of this project.